Star of David theorem

Today we will learn about a very beautiful theorem in geometry -- the Star of David theorem. This theorem is a consequence of the Pascal hexagon theorem and the Pappus theorem.

The butterfly problem

In the previous post, we show a simple proof of the butterfly problem by using Pascal's hexagon theorem. Today, we will list a few more proofs.  These proofs will be presented in the form of exercises so that interested readers can brush up on their problem-solving skills .

Pascal's butterfly

Today we will present a beautiful union between Pascal's hexagon theorem and the butterfly theorem.

Hexagrammum Mysticum Theorem

The mathematician Pascal was most famous for Pascal's triangle, a number pattern that used in the binomial expansion formula. Today, we will introduce a theorem in geometry that bears his name. The Pascal's Hexagrammum Mysticum Theorem states that if we draw a hexagon inscribed in a circle then the three pairs of opposite sides of the hexagon intersect at three points which lie on a straight line.